Particular embodiments generally relate to photolithographic processing and more specifically to a sum of coherent systems (SOCS) approximation optimization.
Lithographic and other processes often have certain signature distortions that fabricate less than optimal features in integrated microdevices. If these distortions can be modeled, the device layout or design can be compensated in anticipation of these fabrication problems. OPC (Optical and Process Correction, or sometimes Optical Proximity Correction) involves making systematic modifications to photomask geometries to increase the achievable resolution and pattern transfer fidelity for photolithography in IC manufacturing. This is accomplished by compensating mask geometry for predictable effects that will occur during imaging or subsequent processing.
A simulation engine is used to provide an accurate simulation of the on-wafer shape, given an input shape on the mask. Conventional simulation engines use the Sum of Coherent Systems (SOCS) approximation, in which on-wafer light intensity for partially coherent illumination is decomposed into an incoherent sum of intensities from a nominally infinite number of coherent systems. The sum of coherent systems (SOCS) approximation may be used to approximate a Hopkins imaging integral. For example, a transmission cross coefficient (TCC) matrix may be decomposed via Eigenvalue decomposition (EVD) into a finite set of kernels (SOCS kernels) whose order of importance in the SOCS series coincides with the magnitude of the respective Eigenvalue. The number of kernels in a SOCS series is large and thus, the SOCS approximation uses only a finite number of kernels, N. The number N is determined to balance accuracy and time taken to compute the sum. For example, the series may be cut off after the first ten or twenty kernels.
The transmission cross coefficients (TCCs) are generated based on the illumination source and projection system being used. Thus, no matter what mask is being used to determine the image intensity, the same finite set of kernels is used. This may be produce results that are not as accurate and/or may not be the most computationally efficient for a particular photomask layout.